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  body: '{"choices":[{"finish_reason":"stop","index":0,"logprobs":null,"message":{"content":"Let \\(t\\) = time (in hours) after the train leaves Station A.\n\n- Train from A speed: \\(60\\text{ km/h}\\)  \n  Distance from A after \\(t\\) hours:  \n  \\[\n  d_A = 60t\n  \\]\n\n- Train from B leaves \\(0.5\\) hours later, speed \\(90\\text{ km/h}\\).  \n  By time \\(t\\), it has been traveling \\(t-0.5\\) hours, so its distance from B is:  \n  \\[\n  d_B = 90(t-0.5)\n  \\]\n\nThey start 300 km apart and move toward each other, so when they meet:\n\\[\nd_A + d_B = 300\n\\]\n\\[\n60t + 90(t-0.5) = 300\n\\]\n\\[\n60t + 90t - 45 = 300\n\\]\n\\[\n150t = 345\n\\]\n\\[\nt = \\frac{345}{150} = 2.3\\text{ hours}\n\\]\n\n### Meeting time\n\\(2.3\\) hours \\(= 2\\) hours \\(+ 0.3\\cdot 60\\) minutes \\(= 2\\) hours \\(18\\) minutes.\n\nSo they meet **2 hours 18 minutes after the first train leaves Station A**  \n(or **1 hour 48 minutes after the second train leaves Station B**).\n\n### Distance from Station A\n\\[\nd_A = 60t = 60(2.3) = 138\\text{ km}\n\\]\n\n**Answer:** They meet **2 h 18 min** after the first departure, **138 km from Station A**.","reasoning":"**Calculating meeting time**\n\nI need to establish relative motion between two trains. Let’s say the first train leaves for t hours, and the second leaves after 0.5 hours. The distances are given by the formulae: from A is 60t, and from B toward A is 90(t-0.5) for t >= 0.5. The total distance to cover is 300 km. \n\nSolving the equation 60t + 90(t-0.5) = 300, I find the meeting time is 2 hours and 18 minutes after the first train departs, and 1 hour and 48 minutes after the second. The distance from A is 138 km.","reasoning_details":[{"format":"openai-responses-v1","index":0,"summary":"**Calculating meeting time**\n\nI need to establish relative motion between two trains. Let’s say the first train leaves for t hours, and the second leaves after 0.5 hours. The distances are given by the formulae: from A is 60t, and from B toward A is 90(t-0.5) for t >= 0.5. The total distance to cover is 300 km. \n\nSolving the equation 60t + 90(t-0.5) = 300, I find the meeting time is 2 hours and 18 minutes after the first train departs, and 1 hour and 48 minutes after the second. The distance from A is 138 km.","type":"reasoning.summary"},{"data":"encrypted_reasoning_REDACTED_1","format":"openai-responses-v1","id":"rs_REDACTED_1","index":1,"type":"reasoning.encrypted"}],"refusal":null,"role":"assistant"},"native_finish_reason":"completed"}],"created":0,"id":"chatcmpl-REDACTED_1","model":"openai/gpt-5.2-20251211","object":"chat.completion","provider":"OpenAI","service_tier":"default","system_fingerprint":null,"usage":{"completion_tokens":510,"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":137},"cost":0.00726775,"cost_details":{"upstream_inference_completions_cost":0.00714,"upstream_inference_cost":0.00726775,"upstream_inference_prompt_cost":0.00012775},"is_byok":false,"prompt_tokens":73,"prompt_tokens_details":{"audio_tokens":0,"cache_write_tokens":0,"cached_tokens":0,"video_tokens":0},"total_tokens":583}}'
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  body: '{"include_reasoning":true,"messages":[{"content":[{"text":"You are a helpful math tutor. Be concise.","type":"text"}],"role":"system"},{"content":"A train leaves Station A at 60 km/h. Another train leaves Station B (300 km away) 30 minutes later at 90 km/h heading toward Station A. At what time do they meet, and how far from Station A? Show your work.","role":"user"},{"content":[{"text":"Let \\(t\\) = time (in hours) after the train leaves Station A.\n\n- Train from A speed: \\(60\\text{ km/h}\\)  \n  Distance from A after \\(t\\) hours:  \n  \\[\n  d_A = 60t\n  \\]\n\n- Train from B leaves \\(0.5\\) hours later, speed \\(90\\text{ km/h}\\).  \n  By time \\(t\\), it has been traveling \\(t-0.5\\) hours, so its distance from B is:  \n  \\[\n  d_B = 90(t-0.5)\n  \\]\n\nThey start 300 km apart and move toward each other, so when they meet:\n\\[\nd_A + d_B = 300\n\\]\n\\[\n60t + 90(t-0.5) = 300\n\\]\n\\[\n60t + 90t - 45 = 300\n\\]\n\\[\n150t = 345\n\\]\n\\[\nt = \\frac{345}{150} = 2.3\\text{ hours}\n\\]\n\n### Meeting time\n\\(2.3\\) hours \\(= 2\\) hours \\(+ 0.3\\cdot 60\\) minutes \\(= 2\\) hours \\(18\\) minutes.\n\nSo they meet **2 hours 18 minutes after the first train leaves Station A**  \n(or **1 hour 48 minutes after the second train leaves Station B**).\n\n### Distance from Station A\n\\[\nd_A = 60t = 60(2.3) = 138\\text{ km}\n\\]\n\n**Answer:** They meet **2 h 18 min** after the first departure, **138 km from Station A**.","type":"text"}],"reasoning_details":[{"format":null,"id":null,"index":0,"summary":"**Calculating meeting time**\n\nI need to establish relative motion between two trains. Let’s say the first train leaves for t hours, and the second leaves after 0.5 hours. The distances are given by the formulae: from A is 60t, and from B toward A is 90(t-0.5) for t >= 0.5. The total distance to cover is 300 km. \n\nSolving the equation 60t + 90(t-0.5) = 300, I find the meeting time is 2 hours and 18 minutes after the first train departs, and 1 hour and 48 minutes after the second. The distance from A is 138 km.","type":"reasoning.summary"},{"data":"encrypted_reasoning_REDACTED_1","format":null,"id":"rs_REDACTED_1","index":1,"type":"reasoning.encrypted"}],"role":"assistant"},{"content":"Now suppose both trains slow down by 10 km/h after traveling half the original distance. When do they meet now?","role":"user"}],"model":"openai/gpt-5.2","reasoning":{"effort":"medium"}}'
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  body: '{"choices":[{"finish_reason":"stop","index":0,"logprobs":null,"message":{"content":"Let \\(t\\) be hours after the train leaves Station A. Stations are 300 km apart. Each train reduces speed by \\(10\\text{ km/h}\\) only **after it has traveled 150 km** (half of 300).\n\n### 1) When do they hit the 150 km mark?\n**Train A:** \\(60\\) km/h  \nTime to go 150 km:\n\\[\n\\frac{150}{60}=2.5\\text{ h}\n\\]\nSo A won’t slow down until \\(t=2.5\\) h.\n\n**Train B:** leaves 0.5 h later at \\(90\\) km/h  \nTime (after B starts) to go 150 km:\n\\[\n\\frac{150}{90}=1.\\overline{6}\\text{ h}\n\\]\nSo B slows down at\n\\[\nt=0.5+1.\\overline{6}=2.166\\overline{6}\\text{ h}\n\\]\n\n### 2) How far apart are they when B slows?\nAt \\(t=2.166\\overline{6}\\):\n\nTrain A distance:\n\\[\nd_A=60(2.166\\overline{6})=130\\text{ km}\n\\]\nTrain B distance:\n\\[\nd_B=150\\text{ km}\n\\]\nTotal covered toward each other: \\(130+150=280\\) km, so remaining distance:\n\\[\n300-280=20\\text{ km}\n\\]\n\n### 3) Finish the last 20 km with new speeds\nAfter \\(t=2.166\\overline{6}\\), speeds are:\n- A still \\(60\\) km/h (has not reached 150 km yet)\n- B becomes \\(80\\) km/h\n\nClosing speed:\n\\[\n60+80=140\\text{ km/h}\n\\]\nTime to close 20 km:\n\\[\n\\frac{20}{140}=\\frac{1}{7}=0.142857\\text{ h}=8.571\\text{ min}\n\\]\n\n### 4) Meeting time\n\\[\nt=2.166\\overline{6}+0.142857=2.3095238\\text{ h}\n\\]\nThat is \\(2\\) hours \\(+\\;0.3095238\\cdot 60 \\approx 18.571\\) minutes \\(\\approx 18\\) min \\(34\\) s.\n\n**They meet about 2 h 18 min 34 s after Train A leaves**  \n(or **1 h 48 min 34 s after Train B leaves**).\n\n(If you also want the meeting location: \\(d_A=60t\\approx 60(2.3095238)=138.57\\) km from Station A.)","reasoning":"**Analyzing train scenarios**\n\nI need to modify the scenario regarding the distance and speeds of the trains. The original distance is 300 km, so interpreting \"half the original distance\" means each train would cover 150 km before slowing down by 10 km/h. I realize each won''t reach 150 km at the same time due to delays. Train A moves at 60 km/h for 2.5 hours before slowing. Train B starts 0.5 hours later, moving initially at 90 km/h. Now, I need to calculate their meeting time considering these speeds.**Calculating meeting time for trains**\n\nIn the original scenario, the trains met at t=2.3 hours, where Train A traveled 138 km and hadn''t hit 150 km yet, so it wouldn''t slow down. However, Train B had traveled 162 km, meaning it did slow after 150 km. With the slowdown considered, I really need to refine the meeting time. From t=0 to 0.5, only Train A is moving; afterward, both trains are in motion. I’ll set up the equations to compute their distances and establish when they’ll meet at 300 km total.**Determining meeting phase for trains**\n\nI need to figure out in which phase the trains meet, likely around t > 2.3 hours. I’ll solve this using piecewise functions. My first guess is that the meeting happens before Train A slows down (t < 2.5) but after Train B does (t > 2.1667). Assuming 2.1667 < t < 2.5, I calculate distances, leading me to t ≈ 2.3095 hours, which is about 2 hours and 18.57 minutes after Train A departs. I also need to confirm that Train B did slow down by that point.**Finding meeting time for trains**\n\nThe statement clarifies that both trains slow down after reaching half the distance, but since Train A hasn''t reached that before the meeting, it won''t slow. Now, I need to figure out the meeting time and also express it in clock time. I can say the meeting occurs 2 hours, 18 minutes, and 34 seconds after Train A departs and 1 hour, 48 minutes, and 34 seconds after Train B leaves. I’ll calculate those key times to ensure everything is correct.","reasoning_details":[{"format":"openai-responses-v1","index":0,"summary":"**Analyzing train scenarios**\n\nI need to modify the scenario regarding the distance and speeds of the trains. The original distance is 300 km, so interpreting \"half the original distance\" means each train would cover 150 km before slowing down by 10 km/h. I realize each won''t reach 150 km at the same time due to delays. Train A moves at 60 km/h for 2.5 hours before slowing. Train B starts 0.5 hours later, moving initially at 90 km/h. Now, I need to calculate their meeting time considering these speeds.**Calculating meeting time for trains**\n\nIn the original scenario, the trains met at t=2.3 hours, where Train A traveled 138 km and hadn''t hit 150 km yet, so it wouldn''t slow down. However, Train B had traveled 162 km, meaning it did slow after 150 km. With the slowdown considered, I really need to refine the meeting time. From t=0 to 0.5, only Train A is moving; afterward, both trains are in motion. I’ll set up the equations to compute their distances and establish when they’ll meet at 300 km total.**Determining meeting phase for trains**\n\nI need to figure out in which phase the trains meet, likely around t > 2.3 hours. I’ll solve this using piecewise functions. My first guess is that the meeting happens before Train A slows down (t < 2.5) but after Train B does (t > 2.1667). Assuming 2.1667 < t < 2.5, I calculate distances, leading me to t ≈ 2.3095 hours, which is about 2 hours and 18.57 minutes after Train A departs. I also need to confirm that Train B did slow down by that point.**Finding meeting time for trains**\n\nThe statement clarifies that both trains slow down after reaching half the distance, but since Train A hasn''t reached that before the meeting, it won''t slow. Now, I need to figure out the meeting time and also express it in clock time. I can say the meeting occurs 2 hours, 18 minutes, and 34 seconds after Train A departs and 1 hour, 48 minutes, and 34 seconds after Train B leaves. I’ll calculate those key times to ensure everything is correct.","type":"reasoning.summary"},{"data":"encrypted_reasoning_REDACTED_2","format":"openai-responses-v1","id":"rs_REDACTED_2","index":1,"type":"reasoning.encrypted"}],"refusal":null,"role":"assistant"},"native_finish_reason":"completed"}],"created":0,"id":"chatcmpl-REDACTED_2","model":"openai/gpt-5.2-20251211","object":"chat.completion","provider":"OpenAI","service_tier":"default","system_fingerprint":null,"usage":{"completion_tokens":1704,"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":1113},"cost":0.0246855,"cost_details":{"upstream_inference_completions_cost":0.023856,"upstream_inference_cost":0.0246855,"upstream_inference_prompt_cost":0.0008295},"is_byok":false,"prompt_tokens":474,"prompt_tokens_details":{"audio_tokens":0,"cache_write_tokens":0,"cached_tokens":0,"video_tokens":0},"total_tokens":2178}}'
